Binary obtained from

Figure 14.12 The phase envelope for the system C02-nC4-nCjousing k j values for the two C02"alkane binaries, obtained from the corresponding data. Experimental data from Nagarajan et al (1990).

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

For all calculations reported here, binary parameters from VLE data were obtained using the principle of maximum likelihood as discussed in Chapter 6, Binary parameters for partially miscible pairs were obtained from mutual-solubility data alone. 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

Appendix C-6 gives parameters for all the condensable binary systems we have here investigated literature references are also given for experimental data. Parameters given are for each set of data analyzed they often reflect in temperature (or pressure) range, number of data points, and experimental accuracy. Best calculated results are usually obtained when the parameters are obtained from experimental data at conditions of temperature, pressure, and composition close to those where the calculations are performed. However, sometimes, if the experimental data at these conditions are of low quality, better calculated results may be obtained with parameters obtained from good experimental data measured at other conditions. 

UNIQUAC Binary Parameters for Noncondensable Components with Condensable Components. Parameters Obtained from Vapor-Liquid Equilibrium Data in the Dilute Region... 

IF BINARY SYSTEM CONTAINS NO ORGANIC ACIDS. THE SECOND VIRTAL coefficients ARE USED IN A VOLUME EXPLICIT EQUATION OF STATE TO CALCULATE THE FUGACITY COEFFICIENTS. FOR ORGANIC ACIDS FUGACITY COEFFICIENTS ARE PREDICTED FROM THE CHEMICAL THEORY FOR NQN-IOEALITY WITH EQUILIBRIUM CONSTANTS OBTAINED from METASTABLE. BOUND. ANO CHEMICAL CONTRIBUTIONS TO THE SECOND VIRIAL COEFFICIENTS. 

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

Xenon dichloride [13780-38-6], XeCl, and xenon(II) chloroduoride [73378-52-6], XeClE, have been prepared by photochemical and electric discharge methods and have been examined at low temperatures by matrix-isolation techniques (39,40). The dichloride has a linear stmcture like that of XeE2. Evidence for the existence of XeCl2, XeBr2, and xenon tetrachloride [14989-42-5], XeCl, has been obtained from Mn ssbauer studies (41,42). Owing to thermal chemical instabiUties, no dihaUde other than the binary duorides has been prepared in macroscopic amounts. 

Iron carbide (3 1), Fe C mol wt 179.56 carbon 6.69 wt % density 7.64 g/cm mp 1650°C is obtained from high carbon iron melts as a dark gray air-sensitive powder by anodic isolation with hydrochloric acid. In the microstmcture of steels, cementite appears in the form of etch-resistant grain borders, needles, or lamellae. Fe C powder cannot be sintered with binder metals to produce cemented carbides because Fe C reacts with the binder phase. The hard components in alloy steels, such as chromium steels, are double carbides of the formulas (Cr,Fe)23Cg, (Fe,Cr)2C3, or (Fe,Cr)3C2, that derive from the binary chromium carbides, and can also contain tungsten or molybdenum. These double carbides are related to Tj-carbides, ternary compounds of the general formula M M C where M = iron metal M = refractory transition metal. 

FreundlicVi-Type Relations A binary Freundlich isotherm, obtained from the ideal adsorbed solution theoiy in loading-explicit closed form [Crittenden et al.. Environ. Sci. TechnoL, 19, 1037 (1985)], is... 

This method involves very simple and inexpensive equipment that could be set up m any laboratory [9, 10] The equipment consists of a 250-mL beaker (used as an external half-cell), two platinum foil electrodes, a glass tube with asbestos fiber sealed m the bottom (used as an internal half-cell), a microburet, a stirrer, and a portable potentiometer The asbestos fiber may be substituted with a membrane This method has been used to determine the fluoride ion concentration in many binary and complex fluondes and has been applied to unbuffered solutions from Willard-Winter distillation, to lon-exchange eluant, and to pyrohydrolysis distil lates obtained from oxygen-flask or tube combustions The solution concentrations range from 0 1 to 5 X 10 M This method is based on complexing by fluonde ions of one of the oxidation states of the redox couple, and the potential difference measured is that between the two half-cells Initially, each cell contains the same ratio of cerium(IV) and cerium(tll) ions... 

The cyclic [SaNs]" cation (5.13), a six r-electron system, is the only example of a nitrogen-rich, binary S-N cation. The thermally stable salt [SaNslaiHgaCle] is obtained from the reaction of (NSC1)3 with HgCla in CHaCla. The bond lengths in the five-membered ring indicate delocalized r-bonding that is attenuated across the S-S bond. 

A list of the systems investigated in this work is presented in Tables 8-10. These systems represent 4 nonpolar binaries, 8 nonpolar/polar binaries, and 9 polar binaries. These binary systems were recognized by Heil and Prausnitz [55] as those which had been well studied for a wide range of concentrations. With well-documented behavior they represent a severe test for any proposed model. The experimental data used in this work have been obtained from the work of Alessandro [53]. The experimental data were arbitrarily divided into two data sets one for use in training the proposed neural network model and the remainder for validating the trained network. 

In order to control the composition of the binary alloy we use the chemical potential pj, and minimize the grand potential Cl. The densities of A and B atoms are obtained from the point distiribution function fj(r) and f2(r) as... 

For a binary mixture the values of x and y can be obtained from the equilibrium curve. Select values of x and read the corresponding value of y from the equilibrium curve. Tabulate values of l/(y - x), and plot versus X], resulting in a graphical integration of the function dx (y - x) [130] between x and xj. This system would have no column internals and no reflux. 

One practical problem of the determinant method is the common unavailability of thermodynamic data and phase diagrams for multiphase compounds. For practical applications, an estimate obtained from data for binary compounds of the multinary system may be useful. 

Characteristic Binary Constants ku Obtained from Volumetric Data... 

By adopting mixing rules similar to those given in Section II, Chueh showed that Eq. (55) can be used for calculating partial molar volumes in saturated liquid mixtures containing any number of components. Some results for binary systems are given in Figs. 7 and 8, which compare calculated partial molar volumes with those obtained from experimental data. 

It is often obtained from Eq. (1.71) when the kernel is assumed to relax much quicker than the solution to be found. Then it is nothing more than a low-density gas approximation to Eq. (1.71), valid when conditions (1.83) or (1.88) are met. For these conditions the differential theory is expected to be binary in collisions, and... 

It is seen that, individually, all the curves appear linear and any one of the five curves might be considered to give accurate quantitative results. However, the actual results that would be obtained from the analysis of a binary mixture containing 10% of one component and 90% of the other, employing detectors with each of the five response factors, is shown in Table 1. 

When the system contains more than one component it is important to be able to explore the distribution of the different components both locally and at long range. One way in which this can be achieved is to evaluate the distribution function for the different species. For example in a binary mixture of components A and B there are four radial distribution functions, g (r), g (r), g (r) and g (r) which are independent under certain conditions. More importantly they would, with the usual definition, be concentration dependent even in the absence of correlations between the particles. It is convenient to remove this concentration dependence by normalising the distribution function via the concentrations of the components [26]. Thus the radial distribution function of g (r) which gives the probability of finding a molecule of type B given one of type A at the origin is obtained from... 

Nitridoborates of lanthanum and the lanthanides were obtained from reactions of lanthanide metal or lanthanide metal nitride with layer-like (a-)BN at elevated temperatures (3>1200°C). These reactions require elaborated techniques in the inert gas sample-handling and the use of efficient heating sources, such as induction heating. Only some compounds remain stable in this high-temperature segment, and the yields of such reactions are often limited due to the competing stability of binary phases, allowing only the most (thermodynamically) stable compounds to exist. 

These simple expressions may also be obtained from the chemical potentials according to Eqs. (XII-26) and (XII-32) by appropriately changing subscripts and recalling that x in these equations represents the ratio of the molar volumes, which in the present case is unity. Owing to the identity of volume fractions with mole fractions in this case, Eqs. (18) and (19) are none other than the chemical potentials for a regular binary solution in which the heat of dilution can be expressed in the van Laar form. The critical conditions (see Eqs. 2)... 

Only two of the four state variables measured in a binary VLE experiment are independent. Hence, one can arbitrarily select two as the independent variables and use the EoS and the phase equilibrium criteria to calculate values for the other two (dependent variables). Let Q, (i=l,2,...,N and j=l,2) be the independent variables. Then the dependent ones, g-, can be obtained from the phase equilibrium relationships (Modell and Reid, 1983) using the EoS. The relationship between the independent and dependent variables is nonlinear and is written as follows... 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

Park has also obtained osmotic coefficient data for the aqueous solutions of NaOH-NaCl- NaAl(OH)4 at 25°C employing the isopiestic method (Park and Englezos, 1999 Park, 1999). The solutions were prepared by dissolving AlCl r6H20 in aqueous NaOH solutions. The osmotic coefficient data were then used to evaluate the unknown Pitzer s binary and mixing parameters for the NaOH-NaCI-NaAl(OH)4-H20 system. The binary Pitzer s parameters, [3(0), P0). and C9, for NaAI(OH)4 were found to be -0.0083, 0.0710, and 0.00184 respectively. These binary parameters were obtained from the data on the ternary system because it was not possible to prepare a single (NaAl(OH)4) solution. 

A novel polysiloxane, containing the isocyanide group pendent to the backbone, has been synthesized. It is observed to react with the metal vapors of chromium, iron and nickel to afford binary metal complexes of the type M(CN-[P])n, where n = 6, 5, 4 respectively, in which the polymer-attached isocyanide group provides the stabilization for the metal center. The product obtained from the reaction with Fe was found to be photosensitive yielding the Fe2(CN-[P])q species and extensive cross-linking of the polymer. The Cr and Ni products were able to be oxidized on exposure of thin films to the air, or electrochemically in the presence of an electron relay. The availability of different oxidation states for the metals in these new materials gives hope that novel redox-active polymers may be accessible. 

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